This is only a guess.
I had same problem with my caravan pump in barrel and it turned out to be the pressure valve in the cold flow pipe, it's white with knurled knob on top , didn't effect toilet pump as that has it's own pump.
Turn the knurled knob clockwise to close the valve, open a cold tap and turn the valve back on until it starts clicking then stop. Check if you have same prob: turn a littlle more anti clockwise.
Hope this helps.
bob
August 2009